Being a western style sheriff, I’m pretty sure Hank’s going to be quite good at handling a bowie knife or similar short, sharp and brutal weapon.

Which means if he gets inside the swing range of that sword (you tend to have to keep someone at arm’s reach with a sword), Princey is going to be backpedalling really fast with a trained knife-fighter in his face.

DING! DING! DING! You got it in one! Don Pardo, tell 3Xp4t what they won!

"They’ve won an all expenses paid vacation of 6 days and 2 nights to scenic Detroit, staying at the newly condemned Hotel 6 on 8 Mile road!! In addition they’ve won a free copy of our home game, a case of Turtle Wax, and a year’s supply of Rice-a-roni, the San Francisco treat!"

You are an expert in the blade, I am not. Further, I am not here for a ‘fair and honourable’ fight, I am here to arrest a criminal. If that criminal resists arrest, as the Gorgon did, I will use lethal force.

(okay, not exactly Faux Old West speak, but that is the essence of how he should reply to the stupid challenge)

He could also toss him a pistol and offer to have a shoot-out, which is just as absurd (and historically only happened very rarely, no matter what Hollywood says)

On top of that, if you are in a fight to the death, being ‘honourable’ about it is quite frankly stupid. Which is WHY there were few actual shootouts.

No, Hank! No, no, no, NO! You’re not there to "prove you’re a man", you’re there to apprehend a wanted criminal. DO NOT fall for the "face me on equal terms" gambit, you have a job to do and an oath to uphold.

It’s a standard trope, the person losing challenges the person winning to a ‘fair fight’s on the grounds that the person winning is a coward, knowing – or at least believing- that they will have an advantage in the ‘fair fight’ (thus it’s still not ‘fair’) and will be able to win or at least escape. The other – often the hero – will agree because they will seek to protect their reputation as brave and honourable.

And apparently, stupid.

Not having seen many real fights I don’t know if it works IRL, but it sure does in fiction. Usually. There are exceptions, like Indiana Jones in Raiders, and Mal Reynolds in Serenity and Firefly.